Crossed Product Algebras for Piece-Wise Constant Functions

Richter, Johan; Silvestrov, Sergei; Ssembatya, Vincent A.; Tumwesigye, Alex Behakanira

doi:10.1007/978-3-319-42105-6_6

Cited by 9 publications

(1 citation statement)

References 4 publications

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“…A description of the structure of representations for the relation (1) and more general families of self-adjoint operators satisfying such relations by bounded and unbounded self-adjoint linear operators on a Hilbert space using reordering formulas for functions of the algebra elements and operators satisfying covariance commutation relation, functional calculus and spectral representation of operators and interplay with dynamical systems generated by iteration of maps involved in the commutation relations have been considered in [4,[8][9][10]12,13,[18][19][20][21][22][39][40][41][42][43][44][46][47][48][49][50][52][53][54][55][56][57][58][59][60][62][63][64][65][66].…”

Section: Introductionmentioning

confidence: 99%

Representations of Polynomial Covariance Type Commutation Relations by Linear Integral Operators on $$L_p$$ Over Measure Spaces

Djinja

Silvestrov

Tumwesigye

2022

Springer Proceedings in Mathematics &Amp; Statistics

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Conditions for linear integral operators on over measure spaces to satisfy the polynomial covariance type commutation relations are described in terms of defining kernels of the corresponding integral operators. Representation by integral operators are studied both for general polynomial covariance commutation relations and for important classes of polynomial covariance commutation relations associated to arbitrary monomials and to affine functions. Representations of the covariance type commutation relations by integral Volterra operators and integral convolution operators are investigated.

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